We have developed a detailed molecular model for the DNA triple helix dT dA dT, in which the helix has three symmetry elements: a pseudodyad relating the Watson-Crick strands, an exact dyad relating the two T strands, and a pseudorotational symmetry relating the Hoogsteen A and T strands. The structure is constrained to a small region of conformation space and has little flexibility. We have obtained crystals of DNA oligonucleotide helices which give fiber type X-ray diffraction patterns. These patterns support our model but indicate that the molecules are ordered only in the axial direction since the usual crystal diffraction spots are not seen. We have obtained and characterized for the first time two-stranded DNA helices with Hoogsteen base pairing. The structural constraints of the duplex are the same as those encountered in modeling the triple helix, of which the Hoogsteen duplex is a component, and serve to determine the structures of both helices. Nearly identical carbonyl vibration spectra of the Hoogsteen duplex is a component, and serve to determine the structures of both helices. Nearly identical carbonyl vibration spectra of the Hoogsteen duplex and the triple helix (both quite different from that of the Watson-Crick duplex) are consistent with the dyad symmetry relating the two pryimidine strands. In reexamining the interaction of poly dT and poly dA we have completed the phase diagram and observed the disproportionation reaction 2 A T ~ A T2 + A, not previously reported in this system. Both the 2 3 and 3 2 transitions have unusually high salt independence, indicating that the DNA triple helix binds more na+ than RNA triplexes, possibly because of closer proximity of the phosphates in the B form DNA helices.